A conventional structure of dual inertial sensors made with bulk-micromachining is shown in FIG. 1. It is made of (100) silicon chips 1, comprising an outer frame 2. The outer frame 2 comprises one or more inner frame 5, and each inner frame 5 is further comprising a proof-mass 3. The proof-mass 3 is connected to the inner frame 5 by a plurality of sensing flexible beams 4, and the inner frame 5 is connected to the outer frame 2 by a plurality of driving flexible beams 6. The sensing beams 4 facilitate the proof-mass 3 to move perpendicular to the surface of the silicon chip defined as z-direction), and the driving beams 6 facilitate the proof-mass 3 to move in parallel to the surface of the silicon chip (defined as y-direction). Two glass sheets (not shown in FIG. 1) are placed on both sides of the silicon chip 1, and connected to the outer frame 2. The thin metal film electrodes 81, 82 are electro-plated on the glass sheets facing the silicon chip surface and corresponding to the two edges of the inner frame 5, respectively. The two thin metal film electrodes 81, 82, with the surface of the inner frame 5, will form edge effect electrostatic driving capacitors c8p, c8n. A thin metal film electrode 9 is electrode-plated on the glass sheets facing the silicon chip surface and the proof-mass 3. The thin metal film electrodes 9, with the surfaces of the proof-mass 3, will form two sensing capacitors c9p, c9n. The alternating driving voltage on the driving capacitors c8p, c8n will make the inner frame 5 and the proof-mass 3 vibrate along y-axis. If there is an angular velocity Ω along x-axis, there will be a Coriolis force F making the proof-mass 3 vibrate along z-axis. The angular rate can be obtained by measuring the amplitude of the z-direction vibration of the proof-mass 3. If there is an acceleration applied along the z-axis, the specific force will move the proof-mass 3 with respect to the inner frame. The acceleration can be obtained by measuring the displacement made by the movement of proof-mass with respect to the inner frame. When the proof-mass 3 moves, the capacitances of the sensing capacitor c9p, c9n will change due to the changes in the capacitor's gap. The displacement of the proof-mass can be obtained by measuring the difference of the capacitances of the capacitors c9p, c9n. As the output signal generated by the angular rate is an alternating signal, and the output signal generated by the acceleration is a low frequency or direct current signal, a signal processing method can be applied to separate the angular rate signal from the acceleration signal.
The proof-mass 3 and its sensing beams form a z-axis mass-spring vibration system. Similarly, the unit, consisting of an inner frame 5, sensing beams 4, and proof-mass 3, together with its driving beams 6, forms a y-axis mass-spring vibration system. As the amplitude of the vibration generated by the driving force of the driver is small, the resonance effect of a vibration system is used to amplify the amplitude. The amplification ratio Q is related to operating frequency and damping coefficient. The closer the operating frequency of the driver is to the resonance frequency of the vibration system, the larger the ratio Q. Similarly, the amplitude generated by the Coriolis force must rely on the resonance effect for amplification. Because the vibration frequency generated by Coriolis force is the same as that of the driving force, the resonance frequency of the sensing axis must be the same as that of the driving axis in order to generate sufficiently large output signals.
The major drawback of the aforementioned sensors is in the manufacturing process of the driving beams. As shown in FIG. 2, the etching is first applied on both sides of the silicon chip. As the speed of silicon wet etching is related to the lattice direction, the etching is slowest along the <111> direction. It is virtually impossible to etch along this direction. Hence, the initial stage of the etching would be as shown in FIG. 2(a). The slant lines represent the (111) facets. If the etching continues, it will proceed along the <110> direction from the intersection of two (111) facets, as shown in FIG. 2(b). FIGS. 2(c)–2(e) show the side views of different stages when both sides of the driving beam are etched. When the etching is perpendicular to the surface, the process should stop and the silicon chips should be removed from the etching solution. However, as there is no automatic mechanism to stop the etching as in the (111) facet, it is hard to control the width of the driving beam. The width of the driving beam affects the coefficient of elasticity, which in turn will affect the resonance frequency. If the width of the driving beam is not accurate, the resonance frequency will be different from that of the sensing beams, and deviate from the original design. For vibration systems with larger Q values, the tolerance of the deviation is smaller. This poses a major problem for the quality of the products.